Redirect existing windows via SSH and X11 forwarding?
Solution 1:
It looks like xpra is an active successor to xmove, and does exactly what you want. The devs bill it as "screen for X clients". While it needs to run on your remote server, it runs just fine out of a home folder. Besides python, xvfb is a runtime dependency.
Once you get it installed on the remote server, it's pretty easy to use.
xpra start :8 --start=xeyes
On your local machine, run:
xpra attach ssh:YOURSERVERHOST:8
Solution 2:
I read on serverfault that you might be able to do that with xmove